The invention can be applied inter alia in the medical field to detect and, if necessary, evaluate for example mitral insufficiencies with the help of the condition of the PIS. Here, also the blood flow coming systolically through the closed mitral valve which, however, is leaking, is decisive. Although data acquired by means of three-dimensional color Doppler sonographic examinations show this undesired reflux, a quantitative evaluation and, hence, the medical relevance is difficult for various reasons. The reflux behind the mitral vale on the side of the atrium, which is also referred to as “jet”, generally has such high flow rates that it is not possible to determine the true velocity of this flow when carrying out a measurement with pulsed ultrasound due to Doppler aliasing. Directly in front of the mitral valve, on the side of the ventricle, a so-called convergence zone forms, which is characterized in that respective layers of the same velocity are generated, which are referred to as PIS (proximal isokinetic shell or proximal isovelocity surface). These layers are superimposed like onion's skin, wherein the magnitude of the velocity increases towards the opening. Due to this layering the gradient of the velocity by definition exists only perpendicularly to the orientation of the surfaces of these skins and, consequently, also the flow rate is known, i.e. perpendicular to the surface of a PIS. If both the surface area (Area A) as well as the magnitude of the velocity are known for a PIS, the flow can be calculated from the product of these two quantities. This method is known as PISA method.
However, it is inherent in all Doppler measurements that it is not possible to measure the respective velocity vector of a flow particle, but only the projection of this velocity vector on the direction of the measuring beam. Thus, only the component of the velocity vector in the direction of the ultrasonic head is known, however not the component perpendicular thereto. If the correct direction of the flow can be acquired from other sources, such as a second ultrasound head, MRI data or vessels' geometry, for example, it is basically possible to carry out an angle correction. In practice, however, when using a color Doppler device, the angle to be corrected may not be much larger than 45° since otherwise the original color Doppler measurement is disturbed too much.
Hitherto known methods of PISA flow measurement do not depart from actually measured PIS forms, but from forms which easily can be modeled mathematically. The prevalent models are a hemisphere and a half-ellipsoid. For example, in the case of a hemisphere, it is sufficient to measure the radius (along the ultrasound beam) in order to calculate the PISA, while in the case of a half-ellipsoid, additionally the lengths of the further semi-axes have to be measured. An example for this is mentioned in Utsunomiya T, Ogawa T, Doshi R, Patel D, Quan M, Henry W L, Gardin J M., Doppler color flow ‘proximal isovelocity surface area’ method for estimating volume flow rate: effects of orifice shape and machine factors. J Am Coll Cardiol. 1991; 17:1103-1111.
In T. Shiota, M. Jones, A. Delabays, X. Li, I. Yamada, M. Ishii, P. Acar, S. Holcomb, N. G. Pandian, and D. J. Sahn, Direct Measurement of Three-dimensionally Reconstructed Flow Convergence Surface Area and Regurgitant Flow in Aortic Regurgitation: In Vitro and Chronic Animal Model Studies. Circulation, Nov. 18, 1997; 96(10): 3687-3695, a semi-quantitative method was described, in which the volume enclosed by a PIS (slice summation) was multiplied by the velocity.
However, the two above-mentioned methods are not sufficiently precise in practice. Due to angle errors between the ultrasound beam and the flow direction the direct measurement of the PIS is generally erroneous: the apparent course of the PIS, i.e. the surface with constant velocity, which can be identified for example by means of the color change in Doppler aliasing, does not correspond to the reality due to this angle error. For example, a PIS which in reality is perfectly hemispherical, is shown e.g. in a shape which approximates a half-ellipsoid in the three-dimensional Doppler dataset. In particular in the case of complexly shaped PIS, such as those that can be caused by a crescent-shaped version of the mitral valve, which cannot be described by means of simple shape models, this leads to significant measurement errors.